Sample size for a diagnostic study

Steve Simon


Categories: Blog post Tags: Confidence intervals Diagnostic testing Sample size justification

*Dear Professor Mean

Dear Jovial,

Sample size is not important. Just ask for enough in the research grant so that you can buy your consulting statistician a new computer. Just kidding. You are actually pretty close to having the right answer.

Power calculations are appropriate only when you have a research hypothesis. The emphasis in a study of a diagnostic test is estimation. You want accurate estimates of sensitivity

**When the focus is on estimation

**For sensitivity and specificity


For example

diagnostic00.gif not found.

where n~a~ and n~n~ are the number of abnormal (diseased) and normal (healthy) patients in the study. You assess abnormal and normal under the gold standard

A sample of size 50 abnormal and 50 normal patients would give a 95% confidence interval of plus/minus 0.12 for Sn and plus/minus 0.083 for Sp. This seems like a reasonable amount of precision. A sample of size 75 in each group would provide slightly narrower confidence intervals (plus/minus 0.098 and plus/minus 0.068 respectively). Your choice of the sample size depends in large part on the number of patients you can recruit from and also a balance between maximizing precision and minimizing the amount of time you spend on this project.

Suppose instead that you wanted to estimate the area under the curve (AUC) for a Received Operating Characteristic Curve (ROC curve). The formula for a standard error here is a bit messier. The web page

offers a JAVAScript calculator for the standard error of the AUC. Let’s suppose that the AUC is going to be around 0.8. With the same 50 abnormal and normal patients


Jovial John wants to know how many subjects to include in a research study of a new diagnostic test. Professor Mean explains that you should select a sample size that will make the confidence interval for sensitivity and/or specificity sufficiently narrow.

You can find an earlier version of this page on my original website.